Résumé:Abstract: The reduced basis element approximation is a discretization method for solving partial differential equations that has inherited features from the domain decomposition method and the reduced basis approximation paradigm in a similar way as the spectral element method has inherited features from domain decomposition methods and spectral approximations. We present here a review of the method directed to the application of fluid flow simulations in hierarchical geometries. We present the rational and the basics of the method together with details on the implementation. We illustrate also the rapid convergence with numerica results.